probably not the alternator if it happens when only turning its gotta be the Power Steering or steering rack make sure everything is greased up could be the PS pump going out
Does this squek vary with speed? When stopped and turning right does it squeak? More info is needed
A Trailblazer that squeaks only when turning to the left could have a problem with the steering or front wheel bearing. Turning to the left puts the right pressure on the parts to cause them to squeak.
Your belt going to the alternator is probably very loose and the motion of the turning alternator is continuing after you turn off the vehicle. Get the belt tightened right away.
The squeaking is caused by friction between two objects that only contact each other during the turning motion of the car - in this case, in the leftward direction. This is an easy fix - stop doing it.
check the battery or battery cables or the alternator or starter
Ball joints.
There are two possibilities when it comes to a squeaking sound when turning. The main reasons are a bad power steering pump, or a steering linkage issue.
Turning mechanical energy into electrical energy The alternator works by turning mechanical energy into electrical energy. When your engine is on, it powers a drive belt that rests on a pulley attached to the alternator. The pulley turns the alternator's rotor shaft, which spins a set of magnets around a coil.
Maybe a bearing is going, a balljoint, or maybe your brakes are catching.
Sounds like your suspension joints are dry or worn out.
The bearings on the alternator could be going bad. Remove the belt from the alternator then spin the alternator by hand to listen for grinding.
check your drive belts